A factory packages coconut water in cone-shaped containers with a base radius of 5.2 cm and a height of 13 cm.The factory designers are currently investigating whether a cone-shaped container can be replaced with a cylinder-shaped container with the same radius and the same total surface area.

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$\frac{\pi {\left(5.2\right)}^2\times 13}{3}$ (M1)

Note: Award (M1) for correct substitution in the volume formula for cone.

368 (368.110…) cm³ (A1)(G2)

Note: Accept 117.173…$\pi$cm³or$\frac{8788}{75}\pi$cm³.

[2 marks]

14.0014…× (5.2) × $\pi$ + (5.2)² ×$\pi$ (M1)(M1)

Note: Award (M1) for their correct substitution in the curved surface area formula for cone; (M1) for adding the correct area of the base. The addition must be explicitly seen for the second (M1) to be awarded. Do not accept rounded values here as may come from working backwards.

313.679… (cm²) (A1)

Note: Use of 3 sf value 14.0 gives an unrounded answer of 313.656….

314(cm²) (AG)

Note: Both the unrounded and rounded answers must be seen for the final (A1) to be awarded.

[3 marks]

2 × $\pi$ × (5.2) × $h$ + 2 ×$\pi$× (5.2)²= 314 (M1)(M1)(M1)

Note: Award (M1) for correct substitution in the curved surface area formula for cylinder; (M1) for adding two correct base areas of the cylinder; (M1) for equating their total cylinder surface area to 314 (313.679…). For this mark to be awarded the areas of the two bases must be added to the cylinder curved surface area and equated to 314. Award at most (M1)(M0)(M0) for cylinder curved surface area equated to 314.

($h$ =) 4.41 (4.41051…) (cm) (A1)(G3)

[4 marks]